Preheat oven to 350°F. Grease a 9×3-inch round cake pan; then, line the pan with parchment paper. (You could also use GOOP*, a homemade pan release.)

In a large bowl, combine the cake mix, 1 egg (reserving the other 2 eggs for later), and 1 stick of melted butter. Stir until well blended.

Pour the mixture into the prepared pan, gently patting it down, and set aside.

In the bowl of a stand mixer on medium speed (or using a hand-held mixer), beat the cream cheese until smooth. Add the remaining 2 eggs and the cocoa powder.

Reducing the mixer to low speed, add the confectioners' sugar. Slowly add the remaining stick of melted butter. Add vanilla and continue to beat the mixture until smooth.

Pour the filling into the pan, over the cake mixture. Bake for 40-50 minutes, being careful not to overbake the cake. The center should still be a little gooey when finished baking.

Let the cake partially cool on a wire rack before cutting and serving.